Spatial Models: Basic Issues * *Basic texts in spatial analysis and econometrics are Cliff and Ord (1973, 1981), Anselin (1988), and Cressie (1993). More recent texts and compilations are Anselin and Florax (1995b), Anselin et al. (2004), Anselin and Rey (2014), LeSage and Pace (2004, 2009), Elhorst (2014), and Arbia (2006, 2014). See also a nice overview of spatial models, and the development of spatial econometrics by Anselin (2002, 2009) and Anselin and Bera (1998).

2017 ◽  
pp. 1-10
Author(s):  
Harry Kelejian ◽  
Gianfranco Piras
2016 ◽  
Vol 36 (1) ◽  
Author(s):  
Daniela Gumprecht

In recent years there were many debates and different opinions whether R&D spillover effects exist or not. In 1995 Coe and Helpman published a study about this phenomenon, based on a panel dataset, that supports the position that such R&D spillover effects are existent. However, this survey was criticized and many different suggestions for improvement came from the scientific community. Some of them were selected and analysed and finally led to a new model. And even though this new model is well compatible with the data, it leads to different conclusions, namely that there doesnot exist an R&D spillover effect. These different results were the motivation to run a spatial analysis, which can be done by considering the countries as regions and using an adequate spatial link matrix. The used methods from the field of spatial econometrics are described briefly and quite general, and finally the results from the spatial models (the ones which correspond to the non-spatial ones) are compared with the results from the non-spatial analysis. The preferred model supports the position that R&D spillover effects exist.


Author(s):  
Stephen Matthews ◽  
Rachel Bacon ◽  
R. L’Heureux Lewis-McCoy ◽  
Ellis Logan

Recent years have seen a rapid growth in interest in the addition of a spatial perspective, especially in the social and health sciences, and in part this growth has been driven by the ready availability of georeferenced or geospatial data, and the tools to analyze them: geographic information science (GIS), spatial analysis, and spatial statistics. Indeed, research on race/ethnic segregation and other forms of social stratification as well as research on human health and behavior problems, such as obesity, mental health, risk-taking behaviors, and crime, depend on the collection and analysis of individual- and contextual-level (geographic area) data across a wide range of spatial and temporal scales. Given all of these considerations, researchers are continuously developing new ways to harness and analyze geo-referenced data. Indeed, a prerequisite for spatial analysis is the availability of information on locations (i.e., places) and the attributes of those locations (e.g., poverty rates, educational attainment, religious participation, or disease prevalence). This Oxford Bibliographies article has two main parts. First, following a general overview of spatial concepts and spatial thinking in sociology, we introduce the field of spatial analysis focusing on easily available textbooks (introductory, handbooks, and advanced), journals, data, and online instructional resources. The second half of this article provides an explicit focus on spatial approaches within specific areas of sociological inquiry, including crime, demography, education, health, inequality, and religion. This section is not meant to be exhaustive but rather to indicate how some concepts, measures, data, and methods have been used by sociologists, criminologists, and demographers during their research. Throughout all sections we have attempted to introduce classic articles as well as contemporary studies. Spatial analysis is a general term to describe an array of statistical techniques that utilize locational information to better understand the pattern of observed attribute values and the processes that generated the observed pattern. The best-known early example of spatial analysis is John Snow’s 1854 cholera map of London, but the origins of spatial analysis can be traced back to France during the 1820s and 1830s and the period of morale statistique, specifically the work of Guerry, d’Angeville, Duplin, and Quetelet. The foundation for current spatial statistical analysis practice is built on methodological development in both statistics and ecology during the 1950s and quantitative geography during the 1960s and 1970s and it is a field that has been greatly enhanced by improvements in computer and information technologies relevant to the collection, and visualization and analysis of geographic or geospatial data. In the early 21st century, four main methodological approaches to spatial analysis can be identified in the literature: exploratory spatial data analysis (ESDA), spatial statistics, spatial econometrics, and geostatistics. The diversity of spatial-analytical methods available to researchers is wide and growing, which is also a function of the different types of analytical units and data types used in formal spatial analysis—specifically, point data (e.g., crime events, disease cases), line data (e.g., networks, routes), spatial continuous or field data (e.g., accessibility surfaces), and area or lattice data (e.g., unemployment and mortality rates). Applications of geospatial data and/or spatial analysis are increasingly found in sociological research, especially in studies of spatial inequality, residential segregation, demography, education, religion, neighborhoods and health, and criminology.


1970 ◽  
Vol 64 (3) ◽  
pp. 772-791 ◽  
Author(s):  
Melvin J. Hinich ◽  
Peter C. Ordeshook

Spatial models of party competition constitute a recent and incrementally developing literature which seeks to explore the relationships between citizens' decisions and candidates' strategies. Despite the mathematical and deductive rigor of this approach, it is only now that political scientists can begin to see the incorporation of those considerations which less formal analyses identify as salient, and perhaps crucial, features of election contests.One such consideration concerns the candidates' objectives. Specifically, spatial analysis often confuses the distinction between candidates who maximize votes and candidates who maximize plurality. Downs and Garvey, for example, assume explicitly that candidates maximize votes, though plurality maximization is clearly the assumption which Garvey actually employs, while Downs frequently assumes that vote maximization, plurality maximization, and the goal of winning are equivalent. Downs, nevertheless, attempts to disentangle these objectives, observing that plurality maximization is the appropriate objective for candidates in a single-member district, while vote maximization is appropriate in proportional representation systems with many parties. All subsequent spatial analysis research, however, assumes either implicitly or explicitly that candidates maximize plurality. If Downs is correct, therefore, this research may not be relevant for a general understanding of electoral competition in diverse constitutional or historical circumstances. The question then is whether those strategies that maximize votes differ from those strategies that maximize plurality.


2019 ◽  
Author(s):  
Timm Betz ◽  
Scott J Cook ◽  
Florian M Hollenbach

The pre-specification of the network is one of the biggest hurdles for applied researchers in undertaking spatial analysis. In this letter, we demonstrate two results. First, we derive bounds for the bias in non-spatial models with omitted spatially-lagged predictors or outcomes. These bias expressions can be obtained without prior knowledge of the network, and are more informative than familiar omitted variable bias formulas. Second, we derive bounds for the bias in spatial econometric models with non-differential error in the specification of the weights matrix. Under these conditions, we demonstrate that an omitted spatial input is the limit condition of including a misspecificed spatial weights matrix. Simulated experiments further demonstrate that spatial models with a misspecified weights matrix weakly dominate non-spatial models. Our results imply that, where cross-sectional dependence is presumed, researchers should pursue spatial analysis even with limited information on network ties.


2010 ◽  
Vol 1 (1) ◽  
pp. 79-98 ◽  
Author(s):  
Michał Bernard Pietrzak

The article presents the problem of the application of the spatial weigh matrix based on economic distance in spatial analysis of the unemployment rate. The spatial weight matrix expresses potential spatial interactions between the researched areas and forms a basis for the instruments applied in spatial econometrics. While identifying the neighbourhood, the following criteria are used: a common border, distance, and the k number of the nearest neighbours. The potential force of impact is identified by means of the standardisation of the matrix by rows to unity, or by means of the distance based on the physical properties of the areas. The disadvantage of the matrix standardisation is the fact of accepting the same force of impact for all the areas. It seems natural is the differentiation of the force of the impact dependent on the selected areas which should result from the differences and similarities of the areas in the scope of the researched phenomenon and its determinants. The use of the distance based on physical properties of the areas allows considering the diverse force of impact of neighbouring areas, which, in turn, allows to obtain a more precise outcome of analyses. Unfortunately, physical properties do not constitute the determinants of economic phenomena covered by a spatial analysis which means that they are not related directly to the scrutinised phenomenon. The application of economic distance for building spatial weight matrix shown in the present paper constitutes a way of determining of the force of impact for the economic spatial processes that is alternative to the distance based on physical properties of the researched areas and to the proposal of the standardisation by rows to unity.


Author(s):  
Simona Mackova

Spatial econometrics presents irreplaceable tool for regional analysis. Omitting additional information about geographical location of observed units could neglect some important influences. The spatial weight matrix W determining neighbourhood relations and degree of influence between observed units belongs to the main components of spatial analysis. Various specification approaches of this non-stochastic matrix could be applied. There is a commonly held belief that spatial regression models are sensitive to spatial weight structure. Some analytics consider it as a myth and points out incorrect interpretation of the model coefficients or misspecified models. Does it really matter what kind of specification is used? This contribution brings an empirical example of several approaches to neighbourhood specification and compares obtained results. According to findings of this analysis, especially spillover effects are incomparable. That confirms unequal performance of spatial structures. The W matrix should be built carefully at the beginning of each spatial analysis task.   


Author(s):  
Martin P. Boer ◽  
Hans-Peter Piepho ◽  
Emlyn R. Williams

Abstract Nearest-neighbour methods based on first differences are an approach to spatial analysis of field trials with a long history, going back to the early work by Papadakis first published in 1937. These methods are closely related to a geostatistical model that assumes spatial covariance to be a linear function of distance. Recently, P-splines have been proposed as a flexible alternative to spatial analysis of field trials. On the surface, P-splines may appear like a completely new type of method, but closer scrutiny reveals intimate ties with earlier proposals based on first differences and the linear variance model. This paper studies these relations in detail, first focussing on one-dimensional spatial models and then extending to the two-dimensional case. Two yield trial datasets serve to illustrate the methods and their equivalence relations. Parsimonious linear variance and random walk models are suggested as a good point of departure for exploring possible improvements of model fit via the flexible P-spline framework.


1976 ◽  
Vol 8 (7) ◽  
pp. 741-752 ◽  
Author(s):  
E S Sheppard

The framework of Bayesian inference is proposed as a structure for unifying those highly disparate approaches to entropy modelling that have appeared in geography to date, and is used to illuminate the possibilities and shortcomings of some of these models. The inadequacy of most descriptive entropy statistics for measuring the information in a spatially-autocorrelated map is described. The contention that entropy maximization in itself provides theoretical justification for spatial models is critically evaluated. It is concluded that entropy should, first and foremost, be regarded as a technique to expand our methods of statistical inference and hypothesis testing, rather than one of theory construction.


Author(s):  
Oscar Luis Alonso Cienfuegos ◽  
Ana Isabel Otero Sánchez

AbstractIn this article we will analyze the results, in terms of population, of the Common Agricultural Policy of the European Union, in a small European region, of one million inhabitants, with geographical characteristics typical of mountain agriculture. We will use spatial econometric techniques to verify whether the hypothesis that public spending destined for direct subsidization contributes positively to the territorial dynamics of certain relevant economic variables is fulfilled, specifically we will study in our case the population variable. From a methodological point of view, we will use several complementary approaches that give solidity to the results, always from the focus of spatial econometrics, essential when working with territorial data at a low level of disaggregation. On the one hand, we will carry out an exploratory spatial data analysis, which will allow us to detect possible patterns of spatial dependence, and then move on to a confirmatory analysis that will consider both, autocorrelation (models of lag and spatial error) and spatial heterogeneity (switching regressions). In addition to this cross-sectional data approach, which is based on a method of estimating the particular to the general, we will also use the estimation of spatial models of panel data, to include a temporal approach, with a method of estimating the general to the particular. The best results are obtained with a Spatial Durbin Model.


ijd-demos ◽  
2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Fauzan Zahid Abiduloh ◽  
Chotib Hasan

Abstract:This research discusses the spatial effects of education and income influences on the 2015 and 2019 Democracy Index of Indonesia. The income variable used is Gross Regional Domestic Product (GRDP) per capita, and the education variable used is the average year of schooling. All of the data are collected from the website of the Indonesian Central Bureau of Statistics, namely www.bps.go.id. Using spatial econometrics, researchers found that the distribution of the democratic index value in each province forms a group spatial systemic pattern. Provinces with high democracy index scores tend to be surrounded by provinces that have high democracy index scores, while provinces with low democracy index scores tend to be surrounded by provinces that have low democracy index scores. Researchers also found a spatial dependence on the influence of education and income on the index of democracy in neighboring provinces. Thus, it can be concluded that the quality of democracy in a province is not only caused by the level of education and income in the province, but also by its neighboring provinces.Keywords: indonesia’s democracy index, education, income, spatial econometrics. Abstrak:Penelitian ini membahas pengaruh spasial variabel pendidikan dan pendapatan terhadap Indeks Demokrasi Indonesia 2015 dan 2019. Variabel pendapatan yang digunakan adalah Produk Domestik Regional Bruto (PDRB) perkapita, dan variabel pendidikan yang digunakan adalah rata-rata lama sekolah. Semua data dikumpulkan dari website Badan Pusat Statistik Indonesia, yaitu www.bps.go.id. Dengan menggunakan ekonometrik spasial, peneliti menemukan bahwa sebaran nilai indeks demokrasi di setiap provinsi membentuk pola sistemik spasial berkelompok. Provinsi dengan skor indeks demokrasi yang tinggi cenderung dikelilingi oleh provinsi yang memiliki skor indeks demokrasi yang tinggi pula, sedangkan provinsi dengan skor indeks demokrasi yang rendah cenderung dikelilingi oleh provinsi yang memiliki skor indeks demokrasi rendah. Peneliti juga menemukan adanya efek spasial dalam pengaruh pendidikan dan pendapatan terhadap indeks demokrasi di provinsi tetangga. Dengan demikian, dapat disimpulkan bahwa kualitas demokrasi di suatu provinsi tidak hanya disebabkan oleh tingkat pendidikan dan pendapatan di provinsi tersebut, tetapi juga oleh provinsi tetangganya.Kata kunci:  indeks demokrasi indonesia, pendidikan, pendapatan, ekonometrika spasial


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